If you let Kenny beat the crap out of you and don't resist, you get the scar immediately. But if he hits you once or twice, but you still beat him, it looks like the scar doesn't appear until episode 4.

Can you post some pictures or link vids where lee has a scar? I haven't seen any, yet.

Scumbag Lee is probably the most well known example I can find. On some scenes, Lee has a scar on his left cheek. You can see it when he threatens the Cancer survivors, when he's about to jump on the Train and especially when he threatens Ben.:p